The different time scales

TAI = International Atomic Time (Temps Atomique International = TAI) is
defined as the weighted average of the time kept by about 200
atomic clocks in over 50 national laboratories worldwide.
TAI-UT1 was approximately 0 on 1958 Jan 1.
UTC = Coordinated Universal Time. Differs from TAI by an integral
number of seconds. When needed, leap seconds are introduced in UTC
to keep the difference between UTC and UT less than 0.9 s.
UTC was introduced in 1972.
UT = Universal time. Defined by the Earth's rotation, formerly determined
by astronomical observations but today GPS satellites are used
instead. This time scale is slightly irregular. There are several
different definitions of UT, but the difference between them is always
less than about 0.03 s.
UT0 = "raw", uncorrected UT as derived from meridian circle observations
or from more modern methods involving GPS satellites.
UT1 = UT0 corrected for polar wandering - usually one means UT1 when
saying UT.
UT2 = UT1 corrected for seasonal variations in the Earth's rotational
speed, by adding
+ 0.022 * sin(2*pi*t) - 0.017 * cos(2*pi*t)
- 0.007 * sin(4*pi*t) + 0.006 * cos(4*pi*t)
seconds to UT1, where t is the fraction of the year (zero at 1 Jan).
UT2 is nowadays considered obsolete.
ET = Ephemeris Time. Was used 1960-1983, and was replaced by TDT and TDB
in 1984. For most purposes, ET up to 1983 Dec 31 and TDT from 1984
Jan 1 can be regarded as a continuous time-scale.
TDT = Terrestial Dynamical Time. Was used 1984-2000 as a time-scale of
ephemerides from the Earth's surface. TDT = TAI + 32.184. Replaced
ET (Ephemeris Time) in 1984, was replaced by TT (Terrestial Time)
in 2001.
TDB = Barycentric Dynamical Time. Used as a time-scale of ephemerides
referred to the barycentre of the solar system. Differs from TDT
by at most a few milliseconds.
TDB = TT + 0.001 658s * sin(g) + 0.000 014s * sin(2*g)
g = 357.53_d + 0.985 600 28_d * ( JD - 245 1545.0 )
(higher order terms neglected; g = Earth's mean anomaly)
TT = Terrestial Time. Originally used instead of TDT or TDB when the
difference between them didn't matter. Was defined in 1991 to be
consistent with the SI second and the General Theory of Relativity.
Replaced TDT in the ephemerides from 2001 and on.
TCG = Geocentric Coordinate Time. Defined in 1991 along with TT
TCB = Barycentric Coordinate Time. Defined in 1991 along with TT
delta-T =
ET - UT prior to 1984
TDT - UT 1984 - 2000
TT - UT from 2001 and on
delta-UT = UT - UTC
DUT = predicted value of delta-UT, rounded to 0.1s, given in some radio
time signals.
GPS time = TAI - 19 seconds. GPS time matched UTC from 1980-01-01
to 1981-07-01. No leap seconds are inserted into GPS time, thus
GPS time is 13 seconds ahead of UTC on 2000-01-01. The GPS epoch
is 00:00 (midnight) UTC on 1980-01-06.
The differences between GPS Time and International Atomic Time (TAI)
and Terrestrial Time (TT), also know as Terrestrial Dynamical Time
(TDT), are constant at the level of some tens of nanoseconds while
the difference between GPS Time and UTC changes in increments of
seconds each time a leap second is added to UTC time scale.
GPS week = a numbering of weeks starting at the GPS epoch 1980-01-06 00:00
GPS time (which back then was equal to UTC). Weeks are numbered from
0 and up until 1023, then it "rolls back" to 0 and are again numbered
from 0 and up, etc. One GPS week rollover cycle is therefore 1024
weeks = 7168 days = ca 19.62 years. So far there's been one such GPS
week number roll-over, on 1999-08-22 00:00 GPS time - a few older GPS
receivers then ceased to show the correct date.
ET 1960-1983
TDT 1984-2000
UTC 1972- GPS 1980- TAI 1958- TT 2001-
----+---------+-------------+-------------------------+-----
| | | |
|<------ TAI-UTC ------>|<----- TT-TAI ----->|
| | | 32.184s fixed |
|<GPS-UTC>|<- TAI-GPS ->| |
| | 19s fixed | |
| |
<> delta-UT = UT1-UTC |
| (max 0.9 sec) |
-----+------------------------------------------------+-----
|<-------------- delta-T = TT-UT1 -------------->|
UT1 (UT) TT/TDT/ET
Older time scales:
GMT = Greenwich Mean Time. It's ambiguous, and is now used (although
not in astronomy) in the sense of UTC in addition to the earlier
sense of UT (in astronomical navigation, GMT still means UT).
Prior to 1925, GMT was reckoned for astronomical purposes from
Greenwich mean noon (12h UT) to avoid a date change in the middle
of the night in Europe - a new GMT date then started 12 hours after
the start of the corresponding civil date. (Prior to 1805 the
Royal Navy Day started 12 hour before local mean solar time, thus
the Royal Navy Day was then approx. 24 hours ahead of GMT).
GCT = Greenwich Civil Time. Used in the US from 1925 to mean the "new"
GMT starting at Greenwich mean midnight, to distinguish it from
the "old" GMT. When UT was adopted, GCT fell out of use.
LMT = Local Mean Time. The mean solar time at the local meridian.
LCT = Local Civil Time, the same as LMT. Used in the US together with GCT.

Delta-T

delta-T varies continuously, depending on the Earth's rotation.

UT1 is variable with respect to UTC. Leap seconds were introduced
in UTC to keep delta-UT within +-0.9s.

TAI-UTC is always an integral number of seconds, and is varied when
leap seconds are added (or removed, but that hasn't happened yet)
at the end of every year, or every half-year, or every third month,
in that order of priority.